A torque converter installed between an engine and an automatic transmission of a vehicle transmits torque between a pump impeller and a turbine runner via a fluid. Since the relative rotation between the pump impeller and the turbine runner increases fuel consumption of the engine, it is preferable to directly connect the pump impeller and the turbine runner soon after the vehicle is started up. A lockup clutch is provided to accomplish this purpose.
In a torque converter provided with a lockup clutch, a change-over between a converter mode where the torque is transmitted via a fluid and a lockup mode where the torque is transmitted via the lockup clutch is performed via a slip mode where a slip in the lockup clutch is allowed such that a part of the torque is transmitted via the fluid while the other part of the torque is transmitted via the lockup clutch. In the slip mode, a hydraulic pressure supplied to the lockup clutch and the engine operation is controlled in order to cause the relative rotation speed of the pump impeller and the turbine runner to gradually become zero.